# Goodness Of Fit Test – Activity #6

Class Activity #6 – Chapter 17 –Chi Square – Hybrid Methods II

Circle One: Monday Wednesday Friday

Your Names (Print) _____________________________________________________________ _____________________________________________________________________________

*Have you ever wondered about the colors of your wardrobe? Do you think various colors occur in equal proportion, or are there more of one color than the others? Let’s find out! I suggest having groups of at least four people for this activity. ***You can do hand-calculation or run the test in SPSS. If you choose to run the test in SPSS, you should enter the color variable into SPSS and skip question #4 & 7. **

- Which chi-square test should you use, goodness of fit or test of independence?
**Why?**

- What is the
__total__number of clothes for your group? (Hint: each of you will randomly pick 10 clothes from your wardrobe)

- Complete the table below:
- For Observed column., count your
__Number Observed__for EACH color of clothing for your group. - In Expected column., tell me the
__number__of EACH color you would__expect__from your group (combine all group members). To calculate this, divide your group’s Total clothing count (from #2) by the number of color categories.*For example, if your group has 40 Total clothing in question 2, then you would*__expect__40/6 = 6.67 clothing of each color). Don’t round up your number to an integer.

- For Observed column., count your

Color | Observed (O) | Expected (E) |

Red | ||

Blue | ||

Yellow | ||

Green | ||

Black/White/Grey | ||

Others | ||

Total |

- (skip if you run your test in SPSS) For the Chi Square test, we compare our “Expectations” to our “Observations”. Complete the chart below for YOUR group’s data from 3

Color |
Observed (O) | Expected (E) | O – E | (O – E)^{2} |
(O – E)^{2} / E |

Red | |||||

Blue | |||||

Yellow | |||||

Green | |||||

Black/White/Grey | |||||

Others | |||||

Total |

- What is your degree of freedom for your Clothing data?

- What is your obtained value of χ
^{2}? That is, what is ∑(O – E)^{2}/E?

- (Skip if you run your test in SPSS) According to Salkind, page 412, the critical value (the value you must overcome based on the chi square table in) is 11.07 for
*p*< .05 and 15.09 for*p*< .01. Is the obtained value you found in #6 more or less than the critical values? Is you chi-square result significant?

- Write up your results as you would see them in a journal style article (Hint: run a descriptive in SPSS for the count and percentage or do hand-calculation)

We ran a _____________________ to determine whether there were equal number of clothing of each color in the group wardrobe. The level is set at .05. The result is _____________, *χ ^{2}*( ) = _____,

*p*________. There were ___( %) red, ___( %) blue, ___ ( %) yellow, ____( %) green, ____( %) black/white/grey, and ____( %) of other color in our sample. In other words, the color of the clothing _________ evenly distributed.